Magnetic compasses utilize a magnetic device to sense and measure orientation within an ambient magnetic field. In the absence of local magnetic anomalies, the ambient magnetic field is the earth's magnetic field. A pendulous mass is commonly used to retain a vertical compass orientation to avoid contamination by the vertical component of the earth's magnetic field. A freely pivoting magnet will align itself with the ambient magnetic field. The compass bearing, .phi., is determined by measuring the angle between the compass case, which rotates in space, and the pivoting internal magnet, which maintains its alignment with the horizontal component of the earth's magnetic field.
If the compass code wheel is not aligned with the internal magnet, the compass output will be biased. Also, magnetic material (other than the single internal magnet) attached to the code wheel assembly will cause a bias in the compass output.
Magnetic material attached to the compass case will rotate around the internal magnet, causing sinusoidal errors in the compass output. The compass internal magnet aligns itself with the vector sum of the earth's field and the field of the magnetic material. The general expression for multiple pieces of magnetic material is: EQU .phi.=.theta.+a+b sin +c cos .theta.
where a is the bias error, discussed above, b and c are the sum of the amplitudes of the orthogonal components of the internal magnetic material, .theta. is the actual bearing of the compass case, and .phi. is the compass output heading.
The errors induced by permanently magnetized material are "one cycle" errors (i.e., functions of sin .theta. and cos .theta.) because the permanently magnetized material amplitude does not change as a function of .theta..
Permeable magnetic material will assume and magnify any field with which it is aligned. Therefore, permeable magnetic material attached to the compass case will rotate around the internal magnet, causing a "two cycle" error (i.e., functions of sin (2.theta.) and cos (2.theta.)) that can be expressed as: EQU .phi.=.theta.+d sin (2.theta.)+e cos (2.theta.)
where d and e are the sum of the maximum amplitudes of the orthogonal components of the internal permeable material. Note that the bias term, the "one cycle" errors, and the "two cycle" errors are all independent of any of the other errors, and therefore, error corrections or calibrations may be considered separately.
A well known method exists for calibrating and removing the compass deviation errors using five correction coefficients: A,B,C,D, and E, as discussed in the Handbook of Magnetic Compass Adjustment, Publication No. 226, Defense Mapping Agency Office, Stock No. NVPUB226, 1980. The A correction is simply the correction for compass bias or offset. The B and C corrections adjust for permanent magnetic anomalies within the compass, and the D and E corrections adjust for induced magnetic anomalies within the compass. The compass deviation correction for actual magnetic head is: EQU deviation correction=A+B sin .phi.+C cos .phi.+D sin 2.phi.+E cos 2.phi.
where .phi. is the compass reading. In order to calculate the deviation coefficients, it is necessary to place the compass on a rotary table with precise angular resolution and a known reference bearing. The compass must be rotated at a constant rate through 360.degree. in each direction while the table bearings and compass bearings are recorded at regular increments and known positions of table bearing.
Another method of data collection is to stop the table at each measurement point and allow the compass gimbal swing to settle out prior to taking data at each point. This alternate procedure is much slower even though only one revolution is required.
When the data is taken on the fly, the method for determining the A, B, C, D, and E coefficients is derived by noting that the average of the differences between the actual compass heading .theta. and the compass reading .phi. is the sum of the average lag and the average deviation: EQU .theta.-.phi.=L+A+B sin .phi.+C cos .phi.+D sin 2.phi.+E cos 2.phi.
The overbar indicates the average over all data points. Since the compass is rotated 360.degree. in each direction at the same rate, L=0. Thus, EQU .theta.-.phi.=A+B sin .phi.+C cos .phi.+D sin 2.phi.+E sin 2.phi.
Since A is constant for all values of .theta., A=.theta.-.phi..
To determine the B coefficient, each of the data points is multiplied by sin .theta.: EQU (.theta.-.phi.) sin .phi.=A sin .phi.+B sin 2.phi.+C sin .phi. cos .phi.+D sin .phi. sin 2.phi.+E sin .phi. cos 2.phi.
The only term on the right side of the equation that is not zero for 360.degree. rotations is EQU B sin (2.phi.)=B/2
Therefore, B=2(.theta.-.phi.) sin .theta.. The same method can be used for computing the C, D, and E coefficients by multiplying each of the data points by cos .phi., sin 2.phi., and cos 2.phi., respectively. That is, EQU B=2(.theta.-.phi.) sin .phi. EQU C=2(.theta.-.phi.) cos .phi. EQU D=2(.theta.-.phi.) sin (2.phi. EQU E=2(.theta.-.phi.) cos (2.phi.
It should be noted that the A error will change if the compass alignment is not preserved in its final mount. The B, C, D, and E errors will vary if the compass is mounted in a magnetic environment that is different from the one in which the compass was calibrated. Finally, the B and C errors vary with latitude.
The requirement of an absolute reference and a precise rotation renders field calibration impractical for most compass applications. Gyro compasses aboard ships have been used for years as a reference for "swing ship" calibrations of magnetic compasses, but gyro errors during maneuvering situations prevent precise calibrations in most cases. Therefore, a simple, accurate, and rapid field calibration apparatus and technique for magnetic compasses are necessary, but not heretofore available.